OpenAxiom is described as ', fork of Axiom , is an open source platform for symbolic, algebraic, and numerical computations' and is an app in the Education & Reference category. There are more than 10 alternatives to OpenAxiom for a variety of platforms, including Windows, Linux, Mac, Online / Web-based and Android. The best alternative is GNU Octave, which is both free and Open Source. Other great apps like OpenAxiom are R (programming language) (Free, Open Source), MATLAB (Paid), Mathematica (Paid) and Scilab (Free, Open Source).
Mathics is a general purpose computer algebra system (CAS) and designed to be a free, light-weight alternative to Mathematica. It's programmable using a Mathematica like language and uses a web interface for user interaction.
GiNaC is a C++ library. It is designed to allow the creation of integrated systems that embed symbolic manipulations together with more established areas of computer science (like computation- intense numeric applications, graphical interfaces, etc.) under one roof.